CN105243432A - NSGA-III-based UPFC (unified power flow controller) location and capacity multi-target configuration method - Google Patents

Abstract

The invention discloses an NSGA-III-based UPFC (unified power flow controller) location and capacity multi-target configuration method. According to the method, with the NSGA-III adopted as a framework, the installation position and capacity of a UPFC are optimized; and a non-dominated solution set is constructed through adopting a reference point-based non-dominated sorting method. Since reference points are uniformly distributed on a hypercube, and niche technology is adopted, and the diversity of populations can be maintained, and the loss of the Pareto optimal solution can be avoided, and a uniform Pareto frontier can be obtained, and problems in UPFC location and capacity multi-target configuration can be well solved.

Description

Based on UPFC addressing and the capacity multiple goal collocation method of NSGA-III

Technical field

Invention belongs to Operation of Electric Systems and control technology field, particularly a kind of new UPFC addressing and capacity multiple goal collocation method.

Background technology

Along with the development of power grid construction, contact more and more tightr between each regional power grid, under current electric grid network structure, it is more difficult to carry out electricity transaction between regional power grid safely.FACTS (flexibleactransmissionsystems, FACTS) is the new technology occurred in recent years.The recent development achievement of power application electronic technology and modern control technology realize AC transmission system parameter so that the control fast flexibly of network structure, realize the reasonable distribution of transmission power together, reduce power attenuation and cost of electricity-generating, increase substantially system stability, reliability.

THE UPFC (unifiedpowerflowconortller, UPFC) be the most complicated in FAFCTS family be also the most attractive a kind of compensator, it combines the flexible control device of many FACTS devices, being considered to the most creative, is powerful FACTS element.Reasonable disposition UPFC is one of emphasis improving transmission system stability, the present invention is with NSGA-III (non-dominated sorted genetic algorithm, nondominatedsortinggeneticalgorithm) be framework, the installation site of UPFC and capacity are optimized, adopt the non-dominated ranking method construct non-dominant disaggregation based on reference point.Due to reference point be uniformly distributed on hypercube, the application of niche technique, maintain the diversity of population, avoid the loss of Pareto optimal solution, obtain uniform Pareto leading surface, solve the problem of UPFC addressing and the configuration of capacity multiple goal preferably.

Summary of the invention

Goal of the invention: the object of the invention is to for the deficiencies in the prior art, provide one can effectively, fast to UPFC addressing and capacity multiple goal collocation method.

For reaching above object, the present invention realizes by the following technical solutions.

The technical solution used in the present invention is:

Based on UPFC addressing and a capacity multiple goal collocation method of NSGA-III, comprise the following steps:

Step 1: the network parameter obtaining electric system, network parameter specifically comprises: bus numbering, title, load are meritorious, reactive load, building-out capacitor, the branch road of transmission line of electricity number, headend node and endpoint node numbering, resistance in series, series reactance, shunt conductance, shunt susceptance, transformer voltage ratio and impedance, generated power is exerted oneself, idle bound of exerting oneself, generator consumption characterisitic parameter, node reference voltage.

Step 2: initialization NSGA-III parameter, specifically comprises: initialization NSGA-III population P _t, population scale N _p, evolutionary generation t=0 is set, maximum evolutionary generation T is set _max.

Step 3:P _tpopulation Q is obtained based on DE evolution (DifferentialEvolution, differential evolution algorithm) _t;

Step 3 specifically comprises the following steps,

Step 301, makes a variation to NSGA-III population:

$v_i^t=x_{r1}^t+F(x_{r2}^t-x_{r3}^t)$

In formula, for the population after variation; F is zoom factor, gets [0,2]; for three Different Individual randomly drawed from population, i is reference point sequence number;

Step 302, interlace operation is carried out to NSGA-III population:

$c_{i,j}^t=\left\{\begin{array}{cccc}{v}_{i,j}^t& rand\left(j\right)\≤C_R& or& j=randn\left(i\right)\\ x_{i,j}^t& rand\left(j\right)>C_R& and& j\≠randn\left(i\right)\end{array}\right.$

In formula, for the population obtained after intersection; Rand (j) is the random number between [0,1]; J is an individual jth component; C _rfor crossover probability; Randn (i) be [1 ..., N _p] between random quantity, N _pfor population scale size;

Obtain the UPFC installation site of Experimental population uPFC capacity

Step 4: to R _t=P _t∪ Q _tquick non-dominated sorting method is adopted to obtain the original non-dominant disaggregation F of different brackets ₁, F ₂..., F _l.

Step 5: obtain non-dominant disaggregation S according to general domination principle _t.

Step 6: compare non-dominant disaggregation S _twith population scale N _psize, if not domination disaggregation S _tbe greater than population scale N _p, then enter step 7, otherwise then evolutionary generation t value adds 1, returns step 3.

Step 7: the reference point Z of setting structure ^s.

Step 8: grade is the non-dominant disaggregation F of l _lself-adaptation normalization, obtains the reference point Z on normalization lineoid ^r;

Step 8 specifically comprises the following steps,

Step 801: the minimum value calculating each objective function

Step 802: objective function is transformed to

Step 803: calculate the limit z on each objective function axle ^{i, max};

Step 804: calculate the intercept α on each objective function axle _i;

Step 805: normalization objective function f _i' (s)

Step 806: according to f _i ⁿx () obtains reference point Z on normalized hypercube ^r.

Step 9:F _lwith Z ^rassociate;

Step 9 specifically comprises the following steps:

Step 901: according to Z ^rdefinition reference line w;

Step 902: calculate F _lthe individual vertical range d to reference line w;

Step 903:F _lwith Z ^rthe reference point be associated and the reference point π corresponding to minimum perpendicular distance d _s.

Step 10: to non-dominant disaggregation S _tcarry out niche reservation operations, obtain population P of future generation _t+1;

Step 10 specifically comprises the following steps,

Step 1001: the niche number of definition i-th reference point is ρ _i;

Step 1002: according to following formula, obtains population P of future generation _t+1:

$P_{t+1}=\left\{\begin{array}{ccc}{P}_{t+1}\∪\underset{s\∈S_t}{\arg \min }\left\{d\left(s\right)\right\}& if& {\mathrm{\ρ}}_j=0\\ P_{t+1}\∪rand\underset{s\∈S_t}{(s:\mathrm{\π}(s)=rand(j:\underset{j\∈Z^r}{\mathrm{argmin}}\left\{{\mathrm{\ρ}}_j\right\}\left)\right)}& if& {\mathrm{\ρ}}_j\≥1\end{array}\right..$

Step 11: compare epicycle evolutionary generation t and T _maxsize, if t>=T _max, then export and obtain UPFC configuration parameter: UPFC controllable voltage source magnitude parameters k _c, UPFC controllable voltage source phase angular dimensions uPFC is idle controling parameters Q _sh; Otherwise, then put iterations t value and add 1, return step 3.

Compared with prior art, beneficial effect of the present invention comprises:

The present invention take NSGA-III as framework, the installation site of UPFC and capacity are optimized, adopt the non-dominated ranking method construct non-dominant disaggregation based on reference point, compared with prior art, the present invention take NSGA-III as framework, the installation site of UPFC and capacity are optimized, adopt the non-dominated ranking method construct non-dominant disaggregation based on reference point.Due to reference point be uniformly distributed on hypercube, the application of niche technique, maintain the diversity of population, avoid the loss of Pareto optimal solution, obtain uniform Pareto leading surface, solve the problem of UPFC addressing and the configuration of capacity multiple goal preferably.

Accompanying drawing explanation

Fig. 1 is the UPFC addressing and the capacity multiple goal collocation method process flow diagram that the present invention is based on NSGA-III;

Fig. 2 is for adopting UPFC transmission system structural representation.

Embodiment

Below in conjunction with accompanying drawing, the present invention is further described.

As shown in Figure 1, a kind of UPFC addressing based on NSGA-III and capacity multiple goal collocation method, comprise the following steps:

Step 1: the network parameter obtaining electric system, comprise: bus numbering, title, load are meritorious, reactive load, building-out capacitor, the branch road of transmission line of electricity number, headend node and endpoint node numbering, resistance in series, series reactance, shunt conductance, shunt susceptance, transformer voltage ratio and impedance, generated power is exerted oneself, idle bound of exerting oneself, generator consumption characterisitic parameter, node reference voltage.

Step 2: initialize routine, comprising: setting NSGA-III Population Size N _p, population scale N _p, maximum evolutionary generation T _max, discrete variable to be optimized is UPFC installation site uPFC capacity initialization NSGA-III population P _t, $P_t=\[x_1^0,...,x_{N_p}^0\],$ Wherein $x_i^0=\[n_p^0,Q_{sh}^0\],$ If evolutionary generation t=0.

Step 3:P _tevolve based on DE and obtain population Q _t, concrete steps are as follows:

Step 301: NSGA-III population is made a variation:

$v_i^t=x_{r1}^t+F(x_{r2}^t-x_{r3}^t)$

In formula: for the population after variation; F is zoom factor, gets [0,2]; for three Different Individual randomly drawed from population.

Step 302: interlace operation is carried out to NSGA-III population:

$c_{i,j}^t=\left\{\begin{array}{cccc}{v}_{i,j}^t& rand\left(j\right)\≤C_R& or& j=randn\left(i\right)\\ x_{i,j}^t& rand\left(j\right)>C_R& and& j\≠randn\left(i\right)\end{array}\right.$

In formula: for the population obtained after intersection; Rand (j) is the random number between [0,1]; J is an individual jth component; C _rfor crossover probability; Randn (i) be [1 ..., N _p] between random quantity, N _pfor population scale size;

Obtain the UPFC installation site of Experimental population uPFC capacity

Step 4: to R _t=P _t∪ Q _tquick non-dominated sorting method is adopted to obtain the original non-dominant disaggregation F of different brackets ₁, F ₂..., F _l;

Step 5: obtain non-dominant disaggregation S according to general domination principle _t, be shown below:

$\left\{\begin{array}{ccc}{P}_{t+1}=S_t,& if& \left|S_t\right|=N_p\\ P_{t+1}={\∪}_{i=1}^{l-1}F,& if& \left|S_t\right|>N_p\end{array}\right..$

Step 6: compare non-dominant disaggregation S _twith population scale N _psize, if not domination disaggregation S _tbe greater than population scale N _p, then jump to step 7, otherwise then evolutionary generation t value adds 1, returns step 3.

Step 7: according to following formula setting H structurized reference point Z ^s:

$H=\left(\begin{array}{c}M+p-1\\ p\end{array}\right)$

In formula, M is the number of objective function, and p is in the halved number of objective function axle.

Step 8: the original non-dominant disaggregation F by grade being l _lself-adaptation normalization, obtains the reference point Z on normalization lineoid ^r, concrete steps are as follows:

Step 801: the minimum value calculating each objective function as follows:

The minimum value of objective function is described as after optimizing:

$\left\{\begin{array}{c}\begin{array}{cc}\min .& F\left(x\right)=\[f_1\left(x\right),f_2\left(x\right),f_3\left(x\right),f_4\left(x\right)\]\end{array}\\ \begin{array}{cc}s.t.& h\left(x\right)=0\end{array}\\ \stackrel{\‾}{g}\≤g\left(x\right)\≤\stackrel{\‾}{g}\end{array}\right.$

Wherein: p _g, Q _rbe respectively generator send out active power and reactive power, θ, V are respectively node voltage phase angle and amplitude, as shown in Figure 2, k _c, be respectively the amplitude controling parameters of UPFC controllable voltage source, Phase angle control parameter, Q _shfor the idle controling parameters of UPFC.F (x) is multiple objective function, generating expense and UPFC investment cost $f_1\left(x\right)=\underset{i}{\Σ}(a_{2i}{P}_{gi}^2+a_{1i}{P}_{gi}+a_{0i})+\frac{1000(a_0{S}^3+a_1{S}^2+a_{2}S)\mathrm{\τ}}{8760},$ Voltage fluctuate index $f_2\left(x\right)=\underset{i=1}{\overset{n}{\Σ}}(U_i-U_i^{ref}),$ Voltage stability index $f_3\left(x\right)=\underset{j\∈N}{\max }\left\{L_j\right\},$ Transient stability index f ₄(x)=V _cr-V _cr0, P _githe active power that i-th generator sends, a _2i, a _1i, a _0ifor consumption family curve parameter, a ₀, a ₁, a ₂for UPFC investment cost constant coefficient, S is the capacity of UPFC, and τ is that present worth such as to turn at the year value coefficient, r is return on electric power investment rate, n _yfor UPFC Economic Life, U _ifor the voltage of node i, for the reference voltage of node i, L _jfor the voltage stability index of node j, V _cr0for not installing the transition energy of UPFC, V _crfor installing the transition energy of UPFC, h (x) is equality constraint; G (x) is inequality constrain; be respectively the upper and lower bound of inequality constrain.

Owing to adding UPFC device in system, need amendment equality constraint h (x), increase inequality constrain g (x).

UPFC node equality constraint is revised as:

In formula: subscript k represents that the UPFC that branch road ij node i end is installed, subscript t represent that branch road ij node j holds the UPFC of installing; Δ P _upfck, Δ Q _upfckbe respectively the i active power of UPFC at node and the amount of unbalance of reactive power of the installing of branch road ij node i end; Δ P _upfct, Δ Q _upfctbe respectively the j active power of UPFC at node and the amount of unbalance of reactive power of the installing of branch road ij node i end; be respectively branch road ij node i end installing UPFC, the active power that node i is injected and reactive power; be respectively active power and the reactive power of the installing of branch road ij node i end UPFC, node j injection; U _upfckfor being provided with the interchange node voltage amplitude of a kth UPFC; U _upfctfor being provided with the interchange node voltage amplitude of t UPFC; J represents and all nodes that the interchange node being provided with a kth UPFC is connected, and j represents that the jth be connected with the interchange node being provided with a kth UPFC exchanges node; U _jfor the jth be connected with the interchange node being provided with a kth UPFC exchanges the voltage magnitude of node; θ _kjit is the phase difference of voltage that the interchange node being provided with a kth UPFC and the jth be attached thereto exchange between node; G _kj, B _kjthe conductance between the interchange node being provided with a kth UPFC and the jth be attached thereto an interchange node and susceptance respectively; J' represents and all nodes that the interchange node being provided with t UPFC is connected, j' represent be connected with the interchange node being provided with t UPFC jth ' individual interchange node; U _j'for be connected with the interchange node being provided with t UPFC jth ' the voltage magnitude of individual interchange node; θ _tj'be the interchange node being provided with t UPFC and the jth be attached thereto ' phase difference of voltage between individual interchange node; G _tj', B _tj'be respectively the interchange node being provided with t UPFC and the jth be attached thereto ' conductance between individual interchange node and susceptance.Δ P _ij, j Δ Q _ijbe respectively UPFC in the injection active power of node i equivalence and reactive power, Δ P _ji, j Δ Q _jibe respectively UPFC in the injection active power of node j equivalence and reactive power, be respectively the voltage phasor of node i, j, for the voltage phasor of UPFC controllable voltage source, for the electric current phasor of UPFC controllable current source, g _ij, b _ijbe respectively the line conductance between node i, j and susceptance, B is the admittance over the ground of circuit.

The inequality constrain increased is:

be respectively f ₁(x), f ₂(x), f ₃(x), f ₄the minimum value of (x).

solve as follows:

Step (a): structure Lagrangian function is as follows:

$L=f\left(x\right)-y^{T}h\left(x\right)-z^T\[g\left(x\right)-l-\underset{\‾}{g}\]-w^T\[g\left(x\right)+u-\stackrel{\‾}{g}\]-\mathrm{\μ}\underset{r^{\′}=1}{\overset{r}{\Σ}}\ln \left(l_{r^{\′}}\right)-\mathrm{\μ}\underset{r^{\′}=1}{\overset{r}{\Σ}}\ln \left(u_{r^{\′}}\right)$

Wherein y=[y ₁..., y _m] ^tfor the Lagrange multiplier of equality constraint, z=[z ₁..., z _r] ^t, w=[w ₁..., w _r] ^tbe respectively the upper and lower limit Lagrange multiplier of inequality constrain, l=[l ₁..., l _r] ^t, u=[u ₁..., u _r] ^tbe respectively the upper and lower limit slack variable of inequality constrain, μ is Discontinuous Factors, and wherein, r' ∈ r, r' represents r' inequality constrain.

Step (b): program initialization, arranges quantity of state initial value, Lagrange multiplier initial value and penalty factor initial value, recovers iteration count k'=1, arranges accuracy requirement 10^-10;

Step (c): definition duality gap C _gap=l ^tz-u ^tw, calculates C _gapvalue and judge C _gapvalue whether meet the accuracy requirement of setting in step (b), if meet, then export result of calculation and stop performing subsequent step, if do not meet, then continuing to perform step (d);

Step (d): calculation perturbation factor mu;

KKT (Karush-Kuhn-Tucker) condition of this problem is:

$\left\{\begin{array}{c}{L}_x={\▿}_{x}f\left(x\right)-{\▿}_{x}h\left(x\right)y-{\▿}_{x}g\left(x\right)(z+w)=0\\ L_y=h\left(x\right)=0\\ L_z=g\left(x\right)-l-\underset{\‾}{g}=0\\ L_w=g\left(x\right)+u-\stackrel{\‾}{g}=0\\ L_l=z-{\mathrm{\μL}}^{-1}e=0\\ L_u=-w-{\mathrm{\μU}}^{-1}e=0\end{array}\right.$

In formula: ▽ _xf (x) for f (x) is to 1 order derivative of x, ▽ _xh (x), ▽ _xg (x) is respectively the Jacobian matrix of h (x), g (x).L＝diag(l ₁,…,l _r)U＝diag(u ₁,…,u _r)Z＝diag(z ₁,…,z _r)W＝diag(w ₁,…,w _r)L ^-1＝diag(1/l ₁,…,1/l _r)，U ^-1＝diag(1/u ₁,…,1/u _r)，e＝[1,…,1] ^T。

Can be in the hope of by latter two equation in formula KKT condition:

μ=(l ^tz-u ^tw)/2r, definition C _gap=l ^tz-u ^tw.

But facts have proved, when the parameter in objective function is poor according to convergence during above formula value, generally adopt

μ＝σC _Gap/2r，

Wherein σ is called Center Parameter, generally gets 0.1, can obtain reasonable convergence in most occasion.

Step (e): the Nonlinear System of Equations in KKT condition can solve by the inferior method of newton-pressgang, by its linearization, can obtain:

$\left[\begin{array}{cc}{H}^{\′}& {\▿}_{x}h\left(x\right)\\ {\▿}_x^{T}h\left(x\right)& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}x\\ \mathrm{\Δ}y\end{array}\right]=\left[\begin{array}{c}{L}_x^{\′}\\ -L_y\end{array}\right]$

$\left[\begin{array}{cc}I& L^{-1}Z\\ 0& I\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}z\\ \mathrm{\Δ}l\end{array}\right]=\left[\begin{array}{c}-L^{-1}{L}_l^{\mathrm{\μ}}\\ L_z+{\▿}_x^{T}g\left(x\right)\mathrm{\Δ}x\end{array}\right]$

$\left[\begin{array}{cc}I& U^{-1}W\\ 0& I\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ}w\\ \mathrm{\Δ}u\end{array}\right]=\left[\begin{array}{c}-U^{-1}{L}_u^{\mathrm{\μ}}\\ -L_w-{\▿}_x^{T}g\left(x\right)\mathrm{\Δ}x\end{array}\right]$

Wherein: Δ x, Δ y, Δ z, Δ l, Δ u, Δ w are the correction of x, y, z, l, u, w, it is one

Mathematic sign, represents the transposition of local derviation.

$L_x^{\′}=L_x+{\▿}_{x}g\left(x\right)\[L^{-1}(L_l^{\mathrm{\μ}}+{\mathrm{ZL}}_z)+U^{-1}(L_u^{\mathrm{\μ}}+{\mathrm{WL}}_w)\]$

$H^{\′}=H-{\▿}_{x}g\left(x\right)\[L^{-1}Z-U^{-1}W\]{\▿}_x^{T}g\left(x\right)$

$H=-\[{\▿}_x^{2}f\left(x\right)-{\▿}_x^{2}h\left(x\right)y-{\▿}_x^{2}g\left(x\right)(z+w)\]$

The above-mentioned three prescription journeys of solving equation can obtain kth ' the correction of secondary iteration.

Step (f): determine that the iteration step length of original variable and dual variable is respectively:

${\mathrm{\&alpha;}}_p=0.9995min\{min(\frac{-l_{r^{\&prime;}}}{{\mathrm{\&Delta;l}}_{r^{\&prime;}}},{\mathrm{\&Delta;l}}_{r^{\&prime;}}<0;\frac{-u_{r^{\&prime;}}}{{\mathrm{\&Delta;u}}_{r^{\&prime;}}},{\mathrm{\&Delta;u}}_r<0),1\}$

${\mathrm{\&alpha;}}_d=0.9995min\{min(\frac{-z_{{}_{r^{\&prime;}}}}{{\mathrm{\&Delta;z}}_{{}_{r^{\&prime;}}}},{\mathrm{\&Delta;z}}_{{}_{r^{\&prime;}}}<0;\frac{-w_{{}_{r^{\&prime;}}}}{{\mathrm{\&Delta;w}}_{{}_{r^{\&prime;}}}},{\mathrm{\&Delta;w}}_r<0),1\}$

Step (g): upgrade original variable and Lagrange multiplier;

$\{\begin{array}{c}{x}^{\left(k^{\&prime;}+1\right)}=x^{\left(k^{\&prime;}\right)}+{\mathrm{\&alpha;}}_p\mathrm{\&Delta;}x\\ l^{\left(k^{\&prime;}+1\right)}=l\left(k^{\&prime;}\right)+{\mathrm{\&alpha;}}_p\mathrm{\&Delta;}l\\ u^{\left(k^{\&prime;}+1\right)}=u^{\left(k^{\&prime;}\right)}+{\mathrm{\&alpha;}}_p\mathrm{\&Delta;}u\end{array},\left\{\begin{array}{c}{y}^{\left(k^{\&prime;}+1\right)}=y^{\left(k^{\&prime;}\right)}+{\mathrm{\&alpha;}}_p\mathrm{\&Delta;}y\\ z^{\left(k^{\&prime;}+1\right)}=z\left(k^{\&prime;}\right)+{\mathrm{\&alpha;}}_p\mathrm{\&Delta;}z\\ w^{\left(k^{\&prime;}+1\right)}=w^{\left(k^{\&prime;}\right)}+{\mathrm{\&alpha;}}_p\mathrm{\&Delta;}w\end{array}\right.$

Step (h): judge whether iterations is greater than K _max, if so, then calculate and do not restrain, quit a program, if not, then put iterations and add 1, return step (c), K _maxbe set to 50.

solve as follows:

Step (a): by following formula to S _tin each population at individual carry out once containing the Load flow calculation of UPFC:

In formula, x=[U, U _upfc, δ, δ _upfc], Δ δ, Δ U, Δ δ _upfc, Δ U _upfcthe meritorious residual delta P of the voltage phase angle of node, voltage magnitude, the voltage phase angle degree of UPFC node, the meritorious residual delta P of node, idle residual delta Q, UPFC node respectively _upfc, idle residual delta Q _upfcas follows:

${\mathrm{\&Delta;P}}_{upfc}=P_{upfc}^s-U_{upfc}\underset{j\&Element;J}{\&Sigma;}{U}_j(G_{kj}{\mathrm{cos\&theta;}}_{kj}+B_{kj}{\mathrm{sin\&theta;}}_{kj})+{\mathrm{\&Delta;P}}_{ij}$

${\mathrm{\&Delta;Q}}_{upfc}=Q_{upfc}^s-U_{upfc}\underset{j\&Element;J}{\&Sigma;}{U}_j(G_{kj}{\mathrm{sin\&theta;}}_{kj}-B_{kj}{\mathrm{cos\&theta;}}_{kj})+{\mathrm{\&Delta;Q}}_{ij}$

The Jacobian matrix of UPFC node is:

$\begin{array}{cc}H=-\frac{\&part;{\mathrm{\&Delta;P}}_{upfc}}{\&part;{\mathrm{\&delta;}}_{upfc}}& J=-\frac{\&part;{\mathrm{\&Delta;P}}_{upfc}}{\&part;U_{upfc}}\end{array}$

$\begin{array}{cc}K=-\frac{\&part;{\mathrm{\&Delta;Q}}_{upfc}}{\&part;{\mathrm{\&delta;}}_{upfc}}& L=-\frac{\&part;{\mathrm{\&Delta;Q}}_{upfc}}{\&part;U_{upfc}}\end{array}$

Step (b): solve voltage stability index:

$L=max\left(L_j\right),L_j=\left|1+\frac{U_{oj}}{U_j}\right|,U_{oj}=-\underset{i\&Element;N_g}{\&Sigma;}{F}_{ji}{U}_i,\left[\begin{array}{c}{U}_l\\ I_g\end{array}\right]=\left[\begin{array}{cc}{Z}_{ll}& F_{\lg }\\ K_{gl}& Y_{gg}\end{array}\right]\left[\begin{array}{c}{I}_l\\ U_g\end{array}\right],$ U _l, I _lfor voltage, the electric current of load bus, U _g, I _gfor voltage, the electric current of generator node.

solve as follows:

Step (a): adopt CUEP method to try to achieve the transition energy V not installing UPFC system _cr0;

Step (b): adopt CUEP method to try to achieve the transition energy V installing UPFC system _cr;

Step (c): can be calculated power system transient stability index f ₄(x)=V _cr-V _cr0.

Step 802: objective function is transformed to

Step 803: calculate the limit z on each objective function axle ^{i, max};

Step 804: calculate the intercept α on each objective function axle _i;

Step 805: normalization objective function f _i' (s)

Step 806: according to f _i ⁿx () obtains reference point Z on normalized hypercube ^r.

Step 9:F _lwith Z ^rassociate, concrete steps are as follows:

Step 901: according to Z ^rdefinition reference line w;

Step 902: calculate F _lthe individual vertical range d to reference line w;

Step 903:F _lwith Z ^rthe reference point be associated and the reference point π corresponding to minimum perpendicular distance d _s.

Step 10: to non-dominant disaggregation S _tcarry out niche reservation operations, obtain population P of future generation _t+1, concrete steps are as follows:

Step 1001: the niche number of definition i-th reference point is ρ _i;

Step 1002: according to following formula, obtains population P of future generation _t+1:

$P_{t+1}=\left\{\begin{array}{ccc}{P}_{t+1}\&cup;\underset{s\&Element;S_t}{\arg \min }\left\{d\left(s\right)\right\}& if& {\mathrm{\&rho;}}_j=0\\ P_{t+1}\&cup;rand\underset{s\&Element;S_t}{(s:\mathrm{\&pi;}(s)=rand(j:\underset{j\&Element;Z^r}{\mathrm{argmin}}\left\{{\mathrm{\&rho;}}_j\right\}\left)\right)}& if& {\mathrm{\&rho;}}_j\&GreaterEqual;1\end{array}\right..$

Step 11: compare this evolutionary generation t and T _maxsize, if t>=T _max, then quitting a program and exporting obtains UPFC configuration parameter: UPFC controllable voltage source magnitude parameters k _c, UPFC controllable voltage source phase angular dimensions uPFC is idle controling parameters Q _sh; Otherwise, then put iterations t value and add 1, return step 3.

The above is only the preferred embodiment of the present invention; be noted that for those skilled in the art; under the premise without departing from the principles of the invention, can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (7)

1., based on UPFC addressing and a capacity multiple goal collocation method of NSGA-III, it is characterized in that: comprise the following steps:

Step 1: the network parameter obtaining electric system;

Step 2: initialization NSGA-III parameter, specifically comprises: initialization NSGA-III population P _t, population scale N _p, evolutionary generation t is set, initialization t=0, maximum evolutionary generation T is set _max;

Step 3:NSGA-III population P _tevolve based on DE and obtain population Q _t;

Step 4: to R _t=P _t∪ Q _tquick non-dominated sorting method is adopted to obtain the original non-dominant disaggregation F of different brackets ₁, F ₂..., F _l;

Step 5: obtain non-dominant disaggregation S according to general domination principle _t;

Step 6: compare non-dominant disaggregation S _twith population scale N _psize, if not domination disaggregation S _tbe greater than population scale N _p, then enter step 7, otherwise then evolutionary generation t value adds 1, returns step 3;

Step 7: the reference point Z of setting structure ^s;

Step 8: grade is the original non-dominant disaggregation F of l _lself-adaptation normalization, obtains the reference point Z on normalization lineoid ^r;

Step 9:F _lwith Z ^rassociate;

Step 10: to non-dominant disaggregation S _tcarry out niche reservation operations, obtain population P of future generation _t+1;

Step 11: compare epicycle evolutionary generation t and T _maxsize, if t>=T _max, then export and obtain UPFC configuration parameter; Otherwise, then put iterations t value and add 1, return step 3.

2. the UPFC addressing based on NSGA-III according to claim 1 and capacity multiple goal collocation method, it is characterized in that, described step 3 specifically comprises the following steps,

Step 301, makes a variation to NSGA-III population:

$v_i^t=x_{r1}^t+F(x_{r2}^t-x_{r3}^t)$

In formula, for the population after variation; F is zoom factor, gets [0,2]; for three Different Individual randomly drawed from population;

Step 302, interlace operation is carried out to NSGA-III population:

$c_{i,j}^t=\left\{\begin{array}{cccc}{v}_{i,j}^t& rand\left(j\right)\&le;C_R& or& j=randn\left(i\right)\\ x_{i,j}^t& rand\left(j\right)>C_R& and& j\&NotEqual;randn\left(i\right)\end{array}\right.$

In formula, for the population obtained after intersection; Rand (j) is the random number between [0,1]; J is an individual jth component; C _rfor crossover probability; Randn (i) be [1 ..., N _p] between random quantity, N _pfor population scale size;

Obtain the UPFC installation site of Experimental population uPFC capacity

3. the UPFC addressing based on NSGA-III according to claim 1 and capacity multiple goal collocation method, is characterized in that,

Step 8 specifically comprises the following steps,

Step 801: the minimum value calculating each objective function

Step 802: objective function is transformed to

Step 803: calculate the limit z on each objective function axle ^{i, max};

Step 804: calculate the intercept α on each objective function axle _i;

Step 805: normalization objective function f _i' (s)

Step 806: according to normalized hypercube obtains reference point Z ^r.

4. the UPFC addressing based on NSGA-III according to claim 1 and capacity multiple goal collocation method, is characterized in that,

Described step 9 specifically comprises the following steps,

Step 901: according to reference point Z ^rdefinition reference line w;

Step 902: calculate F _lthe individual vertical range d to reference line w;

Step 903:F _lwith Z ^rthe reference point π of the reference point be associated corresponding to minimum perpendicular distance d _s.

5. the UPFC addressing based on NSGA-III according to claim 1 and capacity multiple goal collocation method, is characterized in that,

Step 10 specifically comprises the following steps,

Step 1001: the niche number of definition i-th reference point is ρ _i;

Step 1002: according to following formula, obtains population P of future generation _t+1:

$P_{t+1}=\left\{\begin{array}{ccc}{P}_{t+1}\&cup;\underset{s\&Element;S_t}{\arg \min }\left\{d\left(s\right)\right\}& if& {\mathrm{\&rho;}}_j=0\\ P_{t+1}\&cup;rand\underset{s\&Element;S_t}{(s:\mathrm{\&pi;}(s)=rand(j:\underset{j\&Element;Z^r}{\mathrm{argmin}}\left\{{\mathrm{\&rho;}}_j\right\}\left)\right)}& if& {\mathrm{\&rho;}}_j\&GreaterEqual;1\end{array}\right..$

6. the UPFC addressing based on NSGA-III according to claim 1 and capacity multiple goal collocation method, is characterized in that,

Network parameter described in step 1 comprises: bus numbering, title, load are meritorious, reactive load, building-out capacitor, the branch road of transmission line of electricity number, headend node and endpoint node numbering, resistance in series, series reactance, shunt conductance, shunt susceptance, transformer voltage ratio and impedance, generated power is exerted oneself, idle bound of exerting oneself, generator consumption characterisitic parameter, node reference voltage.

7. the UPFC addressing based on NSGA-III according to claim 1 and capacity multiple goal collocation method, is characterized in that,

UPFC configuration parameter described in step 11 comprises UPFC controllable voltage source magnitude parameters k _c, UPFC controllable voltage source phase angular dimensions uPFC is idle controling parameters Q _sh.